I think what I mean by "Aha, this the meaning of the word flooble" is:
"I use the word flooble in everyday life, and I feel comfortable with it. But until now I've never been able to 'play Taboo' with it. Now I can give a substantive definition of how I use it. This will be useful if I need to unpack my utterances for other people (or, conceivably, computers). Also, when people near me in 'language space' use the word flooble, we can compare definitions and possibly dissolve arguments."

So "the meaning" here isn't a definition of the word (all must bow to the mighty power of the definition), but a location of my language along the 'flooble-meaning' axis. To put it another way, the meaning that we "feel" is the one in our (individual) heads. Of course the word has little power if you can't use it for communication --- although we shouldn't underestimate its use in the internal monologue.

In all this, I realise other people may be located at other places along the "meaning-meaning" axis, and mean something else by "Aha, this is the meaning of..." but Doug S., in the comment you link, says:

I've come up with what is, to me, a satisfactory definition of "art"...

which is a more unpacked version of "meaning" than I usually manage.

The second point I want to make is about words being "wrong" --- saying "fish" and meaning to include dolphins, for example.

In a sense, I'm using the top of the post to argue with the bottom of it.

Wondering how to define a word means you're looking at the problem the wrong way—searching for the mysterious essence of what is, in fact, a communication signal.

vs

You come up with a list of things that feel similar, and take a guess at why this is so. But when you finally discover what they really have in common, it may turn out that your guess was wrong. It may even turn out that your list was wrong.

We have two different uses of words here. Firstly, you have a communication signal, which means "When I say this word, I trust that it conjures a picture in your head which is broadly similar to mine." --- so, for example, you can say "go to the shops and get some fish" to your partner, and you know that they'll bring back, not just fish, but the right kind of fish --- or maybe the shop had no fish, so they got crab, or chicken. Of course, they wouldn't argue that they'd brought home fish, but the mental picture painted by the word was sufficient that you are happy with their purchase.

Secondly, you have an academic, informational label, which means "Things whose properties are generally correlated for some underlying reason, so that observations of a large set of these things carry evidence about all of these things." "Is a trout a fish? It has scales and gills, this is good evidence, so we'll accept that it's likely to be a fish. Therefore we guess that it lays eggs." Again, there is an underlying cultural assumption, but the scientific literature makes this explicit. We can actually test whether a dolphin is a (biological) fish, by looking at the properties written in the textbook.

These two uses of words are related, of course, but they are different. In the first case, all you can say about the "meaning" of the word is the dictionary-writer's approach --- roughly how are people using the word? Can we form a better indication of what they mean by it than a list? A use of the word can "fail" in the sense that the idea in the speaker's head hasn't been transmitted to the listener, but apportioning blame in this case is pretty pointless. If we must (in order to avoid the problem in the future, for example), I put the onus on the speaker to ensure that they use words which are appropriate to their current milieu and on the listener to use the milieu to interpret the words. If you have gone back in time and say "I eat fish" and someone presents you with unwanted dolphin-meat, that was your error. If they have come to the present (their future) and say "dolphins are my favourite fish", it's reasonable to update their vocabulary. In either case, adapting the outliers to the population is a reasonably low-cost way of doing business.

In the second use of a word, an authority really has defined the word to mean something, and a use of it can be "wrong" by not matching the definition. We can also ask "is the authority's definition helpful?" which I think is where you're going with "dolphins aren't fish, even if everyone thinks they are". If the textbooks define "fish" in such a way to include dolphins, and then we determine that dolphins don't fit into the same categories as other fish, it's worth taking them out of the category to avoid future confusion.

As a final remark, consider the use of the word "dairy [products]". A good way to start an argument is to ask if this classification includes eggs. (This is pertinent to me, since I'm allergic to both milk and eggs. I want to make sure people don't give me butter, so I say "no dairy products", and then I either say "or eggs" or "including eggs". Experience has shown that neither of these phrasings will avoid an argument.)